Solve for $x$ and $y$ using elimination. ${-2x+3y = 1}$ ${2x-4y = -8}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $-y = -7$ $\dfrac{-y}{{-1}} = \dfrac{-7}{{-1}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {-2x+3y = 1}\thinspace$ to find $x$ ${-2x + 3}{(7)}{= 1}$ $-2x+21 = 1$ $-2x+21{-21} = 1{-21}$ $-2x = -20$ $\dfrac{-2x}{{-2}} = \dfrac{-20}{{-2}}$ ${x = 10}$ You can also plug ${y = 7}$ into $\thinspace {2x-4y = -8}\thinspace$ and get the same answer for $x$ : ${2x - 4}{(7)}{= -8}$ ${x = 10}$